Question

What are the solutions of the equation 9x^4 – 2x^2 – 7 = 0? Use u substitution to solve.

Answer 1

`9x^4 - 2x^2 - 7 = 0 \\ \text{substitution: } x^2=t, \ \ t\ \textgreater \ 0\\ 9t^2-2t-7\ \textgreater \ 0 \\ D=b^2-4ac=(-2)^2-4*9*(-7)=4+252 = 256 \\ t_(1,2)= (-bб √(D) )/(2a)= (2б 16 )/(18) \\ t_1=- (14)/(18) \ \ \ \ \O \\ \boxed{t_2=1} \\ \\x^2=1\\x=б √(1) \\ x=б1`

Answer: x=-1, x=1